CAIRO, April 17 (Reuters) - Former U.S. President Jimmy Carter met leaders from the Islamist movement Hamas from the besieged Gaza Strip at a Cairo hotel on Thursday, his second meeting with Hamas members in three days.

Former Palestinian Foreign Minister Mahmoud al-Zahar and former Interior Minister Saeed Seyam did not speak to reporters at the start of their talks with Carter, who is on a Middle East tour to explore possibilities for peace.

Zahar and Seyam came to Cairo on Wednesday after the Israeli authorities refused to let Carter into Gaza from the Israeli side. Carter has already met a West Bank leader from Hamas and is expected to meet overall leader Khaled Meshaal in Damascus.

Israel and the U.S. administration have criticised Carter's contacts with the movement, which they call a terrorist group.

But Carter argued in Jerusalem that it was counterproductive to exclude Hamas completely from consultations.

Unlike in Israel, his meetings with Hamas are not controversial in Egypt, where the government has had its own talks with the Islamist movement on how to manage the border and how to bring about reconciliation between Hamas and the rival Palestinian faction Fatah.

Hamas has run the Gaza Strip since defeating Fatah forces there in June last year. Palestinian President Mahmoud Abbas, who is also Fatah leader, controls only parts of the West Bank.

Earlier on Thursday, Carter met Egyptian President Hosni Mubarak. No details were available from either side.

Carter won the Nobel Peace Prize in 2002 for his work helping to resolve international conflicts and advance human rights. He brokered a peace treaty between Israel and Egypt -- Israel's first with an Arab neighbour -- which was signed in 1979. (Writing by Jonathan Wright, editing by Will Rasmussen and Mary Gabriel)